In what ways does it do that? I’d say that praying with them legitimizes Catholic Truth, especially as Catholics don’t pray to Allah.
In Mere Christianity, C.S. Lewis writes of a house. All those who believe (who seek Truth) have entered the house, but Christians – and I would say Catholics specifically – have entered the right room, the room at the house’s center. It’s our goal to guide everyone into the right room. Rejecting mutual prayer, ecclesiastical meetings, etc., would hinder this progress, IMO.
I would personally love to pray with Muslims, especially if it’s verbal prayer.
“For which cause God also hath exalted him, and hath given him a name which is above all names: That in the name of Jesus every knee should bow, of those that are in heaven, on earth, and under the earth: And that every tongue should confess that the Lord Jesus Christ is in the glory of God the Father” (Philippians 2:9-11).